# Definition:Second Principle of Mathematical Induction/Induction Hypothesis

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## Terminology of Second Principle of Mathematical Induction

Consider a **Proof by Complete Induction**.

The assumption that $\forall j: n_0 \le j \le k: \map P j$ is true for some $k \in \Z$ is the **induction hypothesis**.

## Also known as

The **induction hypothesis** can also be referred to as the **inductive hypothesis**.